Solve for $k$, $ \dfrac{8}{2k} = -\dfrac{10}{4k} + \dfrac{5k - 10}{k} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2k$ $4k$ and $k$ The common denominator is $4k$ To get $4k$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{8}{2k} \times \dfrac{2}{2} = \dfrac{16}{4k} $ The denominator of the second term is already $4k$ , so we don't need to change it. To get $4k$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{5k - 10}{k} \times \dfrac{4}{4} = \dfrac{20k - 40}{4k} $ This give us: $ \dfrac{16}{4k} = -\dfrac{10}{4k} + \dfrac{20k - 40}{4k} $ If we multiply both sides of the equation by $4k$ , we get: $ 16 = -10 + 20k - 40$ $ 16 = 20k - 50$ $ 66 = 20k $ $ k = \dfrac{33}{10}$